The fine triangle intersections for maximum kite packings

Abstract

In this paper the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let $Fin(v)={(s,t):$ $\exists$ a pair of maximum kite packings of order $v$ intersecting in $s$ blocks and $s+t$ triangles$}$. Let $Adm(v)={(s,t): s+t\leq b_v, s,t$ are non-negative integers$}$, where $b_v=\lfloor v(v-1)/8\rfloor$. It is established that $Fin(v)=Adm(v)\setminus (b_v-1,0),(b_v-1,1)$ for any integer $v\equiv 0,1(\mathrm{mod}8)$ and $v\ge 8$; $Fin(v)=Adm(v)$ for any integer $v\equiv 2,3,4,5,6,7(\mathrm{mod}8)$ and $v\ge 4$.